Empirical Orthogonal Functions

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Missing Values ◽  
Original Data ◽  
Empirical Orthogonal Functions ◽  
Basis Set ◽  
Data Matrix ◽  
Multidimensional Data ◽  
Data Sets ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Multidimensional Data Sets

This chapter focuses on empirical orthogonal functions (EOFs). One of the most useful and common eigen-techniques in data analysis is the construction of EOFs. EOFs are a transform of the data; the original set of numbers is transformed into a different set with some desirable properties. In this sense the EOF transform is similar to other transforms, such as the Fourier or Laplace transforms. In all these cases, we project the original data onto a set of functions, thus replacing the original data with the set of projection coefficients on the chosen new set of basis vectors. However, the choice of the specific basis set varies from case to case. The discussions cover data matrix structure convention, reshaping multidimensional data sets for EOF analysis, forming anomalies and removing time mean, missing values, choosing and interpreting the covariability matrix, calculating the EOFs, projection time series, and extended EOF analysis.

scholarly journals Applying Visual Analysis Procedures to Multidimensional Medical Data

2019 ◽  
Author(s):  
Александр Бондарев ◽  
Aleksandr Bondarev ◽  
Владимир Галактионов ◽  
Vladimir Galaktionov
Keyword(s):  
Preliminary Data ◽  
Visual Analysis ◽  
Original Data ◽  
Medical Data ◽  
Multidimensional Data ◽  
Data Sets ◽  
Data Filtering ◽  
Data Points ◽  
Multidimensional Data Sets

The paper considers the tasks of visual analysis of multidimensional data sets of medical origin. For visual analysis, the approach of building elastic maps is used. The elastic maps are used as the methods of original data points mapping to enclosed manifolds having less dimensionality. Diminishing the elasticity parameters one can design map surface which approximates the multidimensional dataset in question much better. To improve the results, a number of previously developed procedures are used - preliminary data filtering, removal of separated clusters (flotation). To solve the scalability problem, when the elastic map is adjusted both to the region of condensation of data points and to separately located points of the data cloud, the quasi-Zoom approach is applied. The illustrations of applying elastic maps to various sets of medical data are presented.

scholarly journals THE PROCEDURES OF VISUAL ANALYSIS FOR MULTIDIMENSIONAL DATA VOLUMES

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 17-21 ◽  
Author(s):  
A. E. Bondarev
Keyword(s):  
Data Processing ◽  
Visual Analysis ◽  
Original Data ◽  
Multidimensional Data ◽  
Data Sets ◽  
Multidimensional Datasets ◽  
Data Points ◽  
Multidimensional Data Sets

<p><strong>Abstract.</strong> The paper is devoted to problems of visual analysis of multidimensional data sets using an approach based on the construction of elastic maps. This approach is quite suitable for processing and visualizing of multidimensional datasets. The elastic maps are used as the methods of original data points mapping to enclosed manifolds having less dimensionality. Diminishing the elasticity parameters one can design map surface which approximates the multidimensional dataset in question much better. Then the points of dataset in question are projected to the map. The extension of designed map to a flat plane allows one to get an insight about the structure of multidimensional dataset. The paper presents the results of applying elastic maps for visual analysis of multidimensional data sets of medical origin. Previously developed data processing procedures are applied to improve the results obtained - pre-filtering of data, removal of separated clusters (flotation), quasi-Zoom.</p>

Empirical Methods in Short-Term Climate Prediction

2006 ◽  
Author(s):  
Huug van den Dool
Keyword(s):  
Climate Prediction ◽  
Empirical Orthogonal Functions ◽  
Data Sets ◽  
Seasonal Forecasts ◽  
Short Term ◽  
Orthogonal Functions ◽  
Ocean Atmosphere Interaction ◽  
Global Coverage ◽  
Atmosphere Interaction ◽  
Global Data

This clear and accessible text describes the methods underlying short-term climate prediction at time scales of 2 weeks to a year. Although a difficult range to forecast accurately, there have been several important advances in the last ten years, most notably in understanding ocean-atmosphere interaction (El Nino for example), the release of global coverage data sets, and in prediction methods themselves. With an emphasis on the empirical approach, the text covers in detail empirical wave propagation, teleconnections, empirical orthogonal functions, and constructed analogue. It also provides a detailed description of nearly all methods used operationally in long-lead seasonal forecasts, with new examples and illustrations. The challenges of making a real time forecast are discussed, including protocol, format, and perceptions about users. Based where possible on global data sets, illustrations are not limited to the Northern Hemisphere, but include several examples from the Southern Hemisphere.

Identifying VIV Vibration Modes by Use of the Empirical Orthogonal Functions Technique

2002 ◽  
Author(s):  
Gudmund Kleiven
Keyword(s):  
Model Test ◽  
Vibration Mode ◽  
Multivariate Data ◽  
Empirical Orthogonal Functions ◽  
Mode Shapes ◽  
Data Sets ◽  
Vibration Modes ◽  
Ocean Engineering ◽  
Orthogonal Functions ◽  
Related Technique

The Empirical Orthogonal Functions (EOF) technique has widely being used by oceanographers and meteorologists, while the Singular Value Decomposition (SVD being a related technique is frequently used in the statistics community. Another related technique called Principal Component Analysis (PCA) is observed being used for instance in pattern recognition. The predominant applications of these techniques are data compression of multivariate data sets which also facilitates subsequent statistical analysis of such data sets. Within Ocean Engineering the EOF technique is not yet widely in use, although there are several areas where multivariate data sets occur and where the EOF technique could represent a supplementary analysis technique. Examples are oceanographic data, in particular current data. Furthermore data sets of model- or full-scale data of loads and responses of slender bodies, such as pipelines and risers are relevant examples. One attractive property of the EOF technique is that it does not require any a priori information on the physical system by which the data is generated. In the present paper a description of the EOF technique is given. Thereafter an example on use of the EOF technique is presented. The example is analysis of response data from a model test of a pipeline in a long free span exposed to current. The model test program was carried out in order to identify the occurrence of multi-mode vibrations and vibration mode amplitudes. In the present example the EOF technique demonstrates the capability of identifying predominant vibration modes of inline as well as cross-flow vibrations. Vibration mode shapes together with mode amplitudes and frequencies are also estimated. Although the present example is not sufficient for concluding on the applicability of the EOF technique on a general basis, the results of the present example demonstrate some of the potential of the technique.

scholarly journals Variable selection study using Procrustes analysis

2013 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Casimiro S. Munita ◽  
Lúcia P. Barroso ◽  
Paulo M.S. Oliveira
Keyword(s):  
Analytical Techniques ◽  
Procrustes Analysis ◽  
Multidimensional Data ◽  
Data Sets ◽  
Multivariate Statistical ◽  
Data Set ◽  
Essential Information ◽  
Selection Of Variables ◽  
Archaeological Ceramic ◽  
Multidimensional Data Sets

Several analytical techniques are often used in archaeometric studies, and when used in combination, these techniques can be used to assess 30 or more elements. Multivariate statistical methods are frequently used to interpret archaeometric data, but their applications can be problematic or difficult to interpret due to the large number of variables. In general, the analyst first measures several variables, many of which may be found to be uninformative, this is naturally very time consuming and expensive. In subsequent studies the analyst may wish to measure fewer variables while attempting to minimize the loss of essential information. Such multidimensional data sets must be closely examined to draw useful information. This paper aims to describe and illustrate a stopping rule for the identification of redundant variables, and the selection of variables subsets, preserving multivariate data structure using Procrustes analysis, selecting those variables that are in some senses adequate for discrimination purposes. We provide an illustrative example of the procedure using a data set of 40 samples in which were determined the concentration of As, Ce, Cr, Eu, Fe, Hf, La, Na, Nd, Sc, Sm, Th, and U obtained via instrumental neutron activation analysis (INAA) on archaeological ceramic samples. The results showed that for this data set, only eight variables (As, Cr, Fe, Hf, La, Nd, Sm, and Th) are required to interpret the data without substantial loss information.

Imaging, Visualization, and Computation in Developmental Biology

2019 ◽  
Vol 2 (1) ◽  
pp. 223-251 ◽  
Author(s):  
Francesco Cutrale ◽  
Scott E. Fraser ◽  
Le A. Trinh
Keyword(s):  
Data Science ◽  
Molecular Mechanisms ◽  
Cellular Tissue ◽  
Multidimensional Data ◽  
Data Sets ◽  
Cellular Events ◽  
Intact Embryo ◽  
In Vivo Labeling ◽  
Multidimensional Data Sets

Embryonic development is highly complex and dynamic, requiring the coordination of numerous molecular and cellular events at precise times and places. Advances in imaging technology have made it possible to follow developmental processes at cellular, tissue, and organ levels over time as they take place in the intact embryo. Parallel innovations of in vivo probes permit imaging to report on molecular, physiological, and anatomical events of embryogenesis, but the resulting multidimensional data sets pose significant challenges for extracting knowledge. In this review, we discuss recent and emerging advances in imaging technologies, in vivo labeling, and data processing that offer the greatest potential for jointly deciphering the intricate cellular dynamics and the underlying molecular mechanisms. Our discussion of the emerging area of “image-omics” highlights both the challenges of data analysis and the promise of more fully embracing computation and data science for rapidly advancing our understanding of biology.

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